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FROM DIMENSIONAL REDUCTION OF 4d SPIN FOAM MODEL TO ADDING NON-GRAVITATIONAL FIELDS TO 3d SPIN FOAM MODEL
https://doi.org/10.1142/S0219887814500029Cited by:0 (Source: Crossref)
Abstract
A Kaluza–Klein-like approach for a 4d spin foam model is considered. By applying this approach to a model based on group field theory in 4d (TOCY model), and using the Peter–Weyl expansion of the gravitational field, reconstruction of new non-gravitational fields and interactions in the action are found. The perturbative expansion of the partition function produces graphs colored with SU(2) algebraic data, from which one can reconstruct a 3d simplicial complex representing space-time and its geometry (like in the Ponzano–Regge formulation of pure 3d quantum gravity), as well as the Feynman graph for typical matter fields. Thus a mechanism for generation of matter and construction of new dimensions are found from pure gravity.
Keywords:
AMSC: 83C45, 83E15
